How to create a very shallow rounded edges bowl shape in the side of a cylinder?
I would go about it something like this - it's not &quot;parametric&quot; per se, but it's rather easy to implement so it might be a happy trade-off. Since you only need a small influence to the &quot;dent&quot;, I would recommend omitting the subtracting of faces and shrink-wrapping, and instead use Proportional Editing.
First step is to isolate the section of the cylinder where you want the &quot;dent&quot; to be:

Then add enough loop cuts so the individual &quot;cells&quot; are as close to square shape as possible (I take it you've already done this):

Pick a vertex in the center of your &quot;grid&quot; on one side (preferably one of the &quot;cardinal&quot; directions for ease of making the shape later). Turn on Proportional Editing (O), and select one of the edit options from the  top - I recommend Inverse Square (I know &quot;sphere&quot; is selected in the photo - ignore it) however feel free to try different options and see what works best for your project.

Grab the vertex (G) and move it along whatever axis it's aligned to (so it can move towards the center of the cylinder). The size of the blue edit circle controls the size of the edit influence - you can adjust it by scrolling the Mouse Wheel. Move the vertex inwards:

Final shape looks like this (with subdivision surface and smooth shading):